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Cooperation or defection and participation or withdrawal are well-known options of behavior in game-like activities in free societies, yet the co-evolutionary dynamics of these behavioral traits in the individual level are not well…
Evolutionary game theory has proved to be a powerful tool to probe the self-organisation of collective behaviour by considering frequency-dependent fitness in evolutionary processes. It has shown that the stability of a strategy depends not…
The game interactions among individuals in nature are often uncertain and dynamically evolving, significantly influencing the persistence of cooperation. However, it remains a formidable challenge to effectively characterize these dynamic…
We study the population profile in a simple discrete time model of population dynamics. Our model, which is closely related to certain ``bit-string'' models of evolution, incorporates competition for resources via a population dependent…
The coevolutionary dynamics in finite populations currently is investigated in a wide range of disciplines, as chemical catalysis, biological evolution, social and economic systems. The dynamics of those systems can be formulated within the…
The paper presents a model of two-speed evolution in which the payoffs in the population game (or, alternatively, the individual preferences) slowly adjust to changes in the aggregate behavior of the population. The model investigates how,…
The most common assumption in evolutionary game theory is that players should adopt a strategy that warrants the highest payoff. However, recent studies indicate that the spatial selection for cooperation is enhanced if an appropriate…
Demographic noise has profound effects on evolutionary and population dynamics, as well as on chemical reaction systems and models of epidemiology. Such noise is intrinsic and due to the discreteness of the dynamics in finite populations.…
We study fixation in large, but finite, populations with two types, and dynamics governed by birth-death processes. By considering a restricted class of such processes, we derive a continuous approximation for the probability of fixation…
Finite-sized populations of spiking elements are fundamental to brain function, but also used in many areas of physics. Here we present a theory of the dynamics of finite-sized populations of spiking units, based on a quasi-renewal…
Natural selection favors the more successful individuals. This is the elementary premise that pervades common models of evolution. Under extreme conditions, however, the process may no longer be probabilistic. Those that meet certain…
Two mathematical models of macroevolution are studied. These models have population dynamics at the species level, and mutations and extinction of species are also included. The population dynamics are updated by difference equations with…
Synchronization, cooperation, and chaos are ubiquitous phenomena in nature. In a population composed of many distinct groups of individuals playing the prisoner's dilemma game, there exists a migration dilemma: No cooperator would migrate…
We analyse numerically the effects of small population size in the initial transient regime of a simple example population dynamics. These effects play an important role for the numerical determination of large deviation functions of…
Cooperation is a difficult proposition in the face of Darwinian selection. Those that defect have an evolutionary advantage over cooperators who should therefore die out. However, spatial structure enables cooperators to survive through the…
Ecological communities with many species can be classified into dynamical phases. In systems with all-to-all interactions, a phase where a fixed point is always reached and a dynamically-fluctuating phase have been found. The dynamics when…
Standard neutral population genetics theory with a strictly fixed population size has important limitations. An alternative model that allows independently fluctuating population sizes and reproduces the standard neutral evolution is…
We use analytical techniques based on an expansion in the inverse system size to study the stochastic evolutionary dynamics of finite populations of players interacting in a repeated prisoner's dilemma game. We show that a mechanism of…
Phenotype-switching with and without sensing environment is a ubiquitous strategy of organisms to survive in fluctuating environment. Fitness of a population of organisms with phenotype-switching may be constrained and restricted by hidden…
In this paper we study collective decision making on a multi-population, represented by a regular network of groups of individuals. Each group consists of a collection of players and every player can choose between two options. A group is…